Lesson 7.0 - Failure Mechanisms

8/7/2019 Lesson 7.0 - Failure Mechanisms

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Materials EngineeringMMR - 2044

Lesson 7 - Mechanical Failure


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Overview

Failure Modes

Fracture, Fatigue, Creep Fracture Modes

Ductile, Brittle, Intergranular,

Transgranular

Fracture Toughness

Stress Concentration (Flaws)Crack Propagation


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Fracture Modes

Simple fracture is the separation of a bodyinto 2 or more pieces in response to an

applied stress that is static (constant) and attemperatures that are low relative to the Tmof the material.

Classification is based on the ability of amaterial to experience plastic deformation.

Ductile fracture

Accompanied by significant plastic deformation

Brittle fracture

Little or no plastic deformation

Sudden, catastrophic


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Fracture Mechanism

Imposed stress Crack Formation Propagation

Ductile failure has extensive plastic deformation inthe vicinity of the advancing crack. The process

proceeds relatively slow (stable). The crack

resists any further extension unless there is anincrease in the applied stress.

In brittle failure, cracks may spread very rapidly,

with little deformation. These cracks are moreunstable and crack propagation will continue

without an increase in the applied stress.

4


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Ductile vs Brittle Failure

Very

Ductile

Moderately

DuctileBrittle

Fracturebehavior:

Large Moderate%ARor %EL Small Ductile fracture isusually more desirable

than brittle fracture.

Ductile:

Warning before

fracture

Brittle:

No

warning


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Evolution to failure:

Moderately Ductile Failure

neckingvoid

nucleation

Resulting

fracture

surfaces

(steel)

50 mm

particles

serve as void

nucleation

sites.

50 mm

From V.J. Colangelo and F.A. Heiser, Analysis ofMetallurgical Failures(2nd ed.), Fig. 11.28, p. 294, JohnWiley and Sons, Inc., 1987. (Orig. source: P. Thornton, J.Mater. Sci., Vol. 6, 1971, pp. 347-56.)

100 mmFracture surface of tire cord wire loaded in tension.

Courtesy of F. Roehrig, CC Technologies, Dublin, OH.

Used with permission.

fractureCrack

propagation

Coalescence

of cavities


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Ductile failure:-- one piece

-- large deformation

Figures from V.J. Colangelo and F.A. Heiser, Analysis ofMetallurgical Failures(2nd ed.), Fig. 4.1(a) and (b), p. 66 John

Wiley and Sons, Inc., 1987. Used with permission.

Example: Pipe Failures

Brittle failure:-- many pieces

-- small deformations


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Ductile vs. Brittle Failure

cup-and-cone fracture brittle fracture


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(a) SEM image show ing spherical dimplesresulting from a uniaxial tensile load. (b)SEM image ofparabolic dimples from shear

loading. 9

Ductile Failure


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Brittle FractureArrows indicate point at failure origination

Distinctive pattern on the fracture surface: V-

shaped chevron markings point to the failure

origin.


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Transgranular Fracture Cleavage - in most brittle crystalline materials, crack

propagation that results from the repeated breaking

of atomic bonds along specific planes.

This leads to transgranular fracture where the crack

splits (cleaves) through the grains.


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Intergranular(between grains)

304 S. Steel

(metal)

Polypropylene(polymer)

4mm

Intragranular(within grains)

Al Oxide(ceramic)

316 S. Steel

(metal)

3mm

160mm

1mm

Various Failure Modes


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Fracture Mechanics

Studies the relationships

between:material properties,

stress level,crack producing flaws, and

crack propagationmechanisms.

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Stress Concentration

The measured fracture strengths for mostbrittle materials are significantly lower thanthose predicted by theoretical calculationsbased on atomic bond energies.

This discrepancy is explained by thepresence of very small, microscopic flaws or

cracks that are inherent to the material. The flaws act as stress concentrators or

stress raisers, amplifying the stress at a

given point. This localized stress diminishes with distance

away from the crack tip.


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Flaws are Stress Concentrators

If crack is similar to elliptical hole

through plate, and is oriented

perpendicular to applied stress,

the maximum stress m=

where

t= radius of curvature

o= applied stressm= stress at crack tip

a = length of surface crack or

length of internal crack

m/o= Kt the stress concentration factor

m 2oa

t

1/ 2

Kto

t


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Engineering Fracture Design

r/h

sharper fillet radius

increasing w/h

0 0.5 1.01.0

1.5

2.0

2.5

Stress Conc. Factor, Kt=

Stress concentration can result from sharp corners

Adapted from Fig. 8.2W(c), Callister 6e.(Fig. 8.2W(c) is from G.H. Neugebauer,

Prod. Eng. (NY), Vol. 14, pp. 82-871943.)

r,

filletradius

w

h

o

max

max

0


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Redesigning


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1. What is the magnitude of the maximumstress that exists at the tip of an internalcrack having a radius of curvature of 2.5 x10-4 mm and a crack length of 2.5 x 10-2

mm when a tensile stress of 170 MPa isapplied?

2. Estimate the theoretical fracture strengthof a brittle material if it is known thatfracture occurs by the propagation of anelliptically shaped surface crack of length

0.25 mm and having a tip radius ofcurvature of 1.2 x 10-3 mm when a stressof 1200 MPa is applied.


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Ductile vs Brittle

The effect of a stress raiser is moresignificant in brittle than in ductile materials.

For a ductile material, plastic deformationresults when the maximum stress exceedsthe yield strength.

This leads to a more uniform distribution ofstress in the vicinity of the stress raiser; themaximum stress concentration factor will beless than the theoretical value.

In brittle materials, there is no redistributionor yielding.


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Critical Stress

All brittle materials contain a population ofsmall cracks and flaws that have a varietyof sizes, geometries and orientations.

When the magnitude of a tensile stress atthe tip of one of these flaws exceeds thevalue of this critical stress, a crack forms

and then propagates, leading to failure. Fracture toughness measures a materials

resistance to brittle fracture when a crack

is present.

21


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Fracture Toughness Dependence on

Critical Stress for Crack Propagation

The critical stress for crack propagation in brittle

materials:

where E= modulus of elasticity

s = specific surface energy a= one half length of internal crack

For ductile => replace sby s+ pwhere p is plasticdeformation energy

212

/

sc

a

E


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Crack growth condition:

Largest, most stressed cracks grow first.

Fracture Toughness (Kc

)

Kc = aY

-- Result 1: Max. flaw sizedictates design stress.

max

cdesign

aYK

amaxnofracture

fracture

-- Result 2: Design stressdictates max. flaw size.

2

1

design

cmax

YKa

amax

nofracture

fracture


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Fracture Cracks


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Crack Surface Displacement

(a) mode I, opening or tensile;(b) mode II, sliding;

(c) mode III, tearing;


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Loading Rate

Increased loading rate...-- increases yand TS

-- decreases %EL

Why? An increased rategives less time for

dislocations to move pastobstacles.

y

y

TS

TS

larger

smaller


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Fracture Toughness


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Two designs to consider...

Design A

-- largest flaw is 9 mm-- failure stress = 112 MPa

Design B

-- use same material-- largest flaw is 4 mm

-- failure stress = ?

Key point: Yand Kcare the same in both designs.

Answer: MPa168)( B c Reducing flaw size pays off.

Material has Kc= 26 MPa-m0.5

Design Example: Aircraft Wing

Use...

max

cc

aY

K

BmaxAmax aa cc

9 mm112 MPa 4 mm-- Result:


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Crack Propagation

Cracks propagate due to sharpness of crack tip

A plastic material deforms at the tip, blunting

the crack.deformedregion

brittle

Energy balance on the crack

Elastic strain energy-

energy stored in material as it is elastically deformed this energy is released when the crack propagates

creation of new surfaces requires energy

plastic


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Brittle Fracture of Ceramics

Most ceramics

(at room

temperature)

fracture beforeany plastic

deformation can

occur. Typical crack

configurations

for 4 commonloading

methods.


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Brittle Fracture of Ceramics

Surface of a 6-mm

diameter fused silica rod.

Characteristic fracturebehavior in ceramics

Origin point

Initial region (mirror) is flat

and smooth After reaches critical

velocity crack branches

mist

hackle


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Fracture of Polymers

fibrillar bridges microvoids crack

aligned chains

The fracture strengths of polymers are low relative to ceramics andmetals.

The fracture mode in thermosetting polymers (heavily crosslinked

networks) is typically brittle.

Forthermoplastic polymers, both ductile and brittle modes are possible.

Reduced temperature, increased strain rate, sharp notches, increased

specimen thickness are some factors that can influence a brittle fracture.

One phenomenon that occurs in thermoplastics is crazing, very localized

plastic deformation and formation of microvoids and fibrillar bridges


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3333

Impact Testing

final height initial height

Impact loading:-- severe testing case

-- makes material more brittle

-- decreases toughness

(Charpy)


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Pre-WWII: The Titanic WWII: Liberty ships

Ductile to Brittle Transition Temperature (DBTT)

Disastrous consequences for a welded transport ship,

suddenly split across the entire girth of the ship (4C).

The vessels were constructed from steel alloys that

exhibit a DBTT room temp


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Charpy Impact Energy (A) and Shear Fracture

% (B) Correlated with Temperature


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Steel Charpy Samples

Fracture surfaces after impact showingthe variation in ductility with testing

temperature (C).


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Increasing temperature...-- increases %EL and Kc

Ductile-to-Brittle Transition Temperature (DBTT)...

Temperature

BCC metals (e.g., iron at T< 914C)

ImpactEnergy

Temperature

High strength materials (y> E/150)

polymers

More DuctileBrittle

Ductile-to-brittletransition temperature

FCC metals (e.g., Cu, Ni)


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Fatigue

Fatigue is a form of failure that occurs in structuressubjected to dynamic stresses over an extended period.

Under these conditions it is possible to fail at stress levels

considerably lower than tensile or yield strength for a static

load.Single largest cause of failure in metals; also affects

polymers and ceramics (not glass).

Common failure in bridges, aircraft and machine

components.

Fatigue testing apparatus for rotating bending test

C li St F

ti


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Variation of stress with time thataccounts for fatigue failures.

The stress may be axial (tension-

compression), flexural (bending)

or torsional (twisting) in nature.

There are 3 fluctuating stress-

time modes seen in the figure:

(a) reversed stress cycle -

symmetrical amplitude about a

mean zero stress level; (b)

repeated stress cycle -

asymmetrical maxima and

minima relative to the zero stress

level; (c) variable (random)

stress level

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Cyclic Stress - Fatigue

Fatig e


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Fatigue Fracture surface with

crack initiation at top.Surface shows

predominantly dull

fibrous texture where

rapid failure occurred

after crack achievedcritical size.

Fatigue failure

1. Crack initiation2. Crack propagation

3. Final failure


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Fatigue failure is

brittle in nature,

even in normally

ductile materials;

there is very little

plastic deformation

associated with the

failure.

The image shows

fatigue striations

(microscopic).

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Crack grows incrementally

typ. 1 to 6

a~ increase in crack length per loading cycle

Failed rotating shaft

-- crack grew even though

Kmax< Kc-- crack grows faster as

increases crack gets longer loading freq. increases.

crack origin

Adapted from

Fig. 9.28, Callister &Rethwisch 3e. (Fig.9.28 is from D.J.

Wulpi, UnderstandingHow Components Fail,American Society for

Metals, Materials Park,

OH, 1985.)

Fatigue Mechanism

mK

dN

da

S N C


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A specimen is subjected to stress cycling at a maximum stress

amplitude; the number of cycles to failure is determined.

This procedure is repeated on other specimens at progressively

decreasing stress amplitudes. Data are plotted as stress S versus number N of cycles to failure for all

the specimen.

Typical S-N behavior: the higher the stress level, the fewer the number

of cycles. 44

S-N Curves

F ti Li it


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For some iron and titanium alloys, the S-N curve becomes horizontal

at higher number of cycles N.

Essentially it has reached a fatigue limit, and below this stress level

the material will not fatigue.

The fatigue limit represents the largest value of fluctuating stress

that will not cause failure for an infinite number of cycles.45

Fatigue Limit

Fatigue Curves for Polymers


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Fatigue Curves for Polymers


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During machining operations, small scratches

and grooves can be introduced; these can

limit the fatigue life.

Improving the surface finish by polishing will

enhance fatigue life significantly. One of the most effective methods of

increasing fatigue performance is by imposing

residual compressive stresses within a thin

outer surface layer. A surface tensile stress

will be offset by the compressive stress.

Shot peening (localized plastic deformation)

with small (diameters ranging from 0.1 to 1.0

mm), hard particles (shot) are projected at

high velocities on to the surface. The resulting

deformation induces compressive stresses to

a depth of roughly to of the shot

diameter.

The influence of shot peening is compared in

the graph. 47

Surface Treatments

C H d i


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Case Hardening Case hardening is a

technique where both

surface hardness and

fatigue life are improved

for steel alloys.

Both core region and

carburized outer case

region are seen in image.

Knoop microhardness

shows case has higherhardness (smaller indent).

A carbon or nitrogen rich

outer surface layer (case)

is introduced by atomic

diffusion from thegaseous phase. The case

is typically 1mm deep and

is harder than the inner

core material.

f


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Improving Fatigue Life

1. Impose a compressive

surface stress(to suppress surface

cracks from growing)

N = Cycles to failure

moderate tensile mLarger tensile m

S = stress amplitude

near zero or compressive mIncreasing

m

--Method 1: shot peening

putsurface

intocompression

shot--Method 2: carburizing

C-rich gas

2. Remove stress

concentrators.bad

bad

better

better

C


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Creep

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Materials are often placed in service at elevated

temperatures (>0.4 Tm) and exposed to static

mechanical stresses.

Examples are turbine rotors in jet engines and steamgenerators that experience centrifugal stresses and

high pressure steam lines.

Creep is time dependent, permanent deformation of the

material when subjected to a constant load or stress.

Creep


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Creep

Creep strain vs time at constant load and

constant elevated temperature. Minimum creep

rate (steady-state creep rate), is the slope of

the linear segment in the secondary region.

Rupture lifetime tr is the total time to rupture.

A typical creep test consists of

subjecting a specimen to a

constant load or stress while

maintaining constant temperature.

Upon loading, there is instantelastic deformation. The resulting

creep curve consists of 3 regions:

primary or transient creep adjusts

to the creep level (creep rate maydecrease); secondary creep-

steady state-constant creep rate,

fairly linear region (strain

hardening and recovery stage);

tertiary creep, there is acceleratedrate of strain until rupture (grain

boundary separation, internal

crack formation, cavities and

voids).

C


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CreepSample deformation at a constant stress () vs. time

Primary Creep: slope (creep rate)

decreases with time.

Secondary Creep: steady-state

i.e., constant slope.

Tertiary Creep: slope (creep rate)

increases with time, i.e. acceleration of rate.

0 t

Creep


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Creep

Dependence of creep strain rate on stress; stress versus rupture

lifetime for a low carbon-nickel alloy at 3 temperatures.

S d C


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Strain rate is constant at a given T, -- strain hardening is balanced by recovery

stress exponent (material parameter)

strain rate

activation energy for creep

(material parameter)

applied stressmaterial const.

Strain rate

increases

for higherT,

10

20

40

100

200

10-2 10-1 1Steady state creep rate (%/1000hr)

s

Stress (MPa)427C

538 C

649C

RT

QK cns exp2

Secondary Creep

SUMMARY


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Engineering materials don't reach theoretical strength.

Flaws produce stress concentrations that cause

premature failure.

Sharp corners produce large stress concentrations

and premature failure.

Failure type depends on Tand stress:

- for noncyclic and T< 0.4Tm, failure stress decreases with:- increased maximum flaw size,

- decreased T,- increased rate of loading.

- for cyclic :- cycles to fail decreases as increases.

- for higherT(T> 0.4Tm):- time to fail decreases as orTincreases.

SUMMARY

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Lesson 7.0 - Failure Mechanisms

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